Problem: The equation of an ellipse $E$ is $\dfrac {(y-6)^{2}}{9}+\dfrac {(x-6)^{2}}{36} = 1$. What are its center $(h, k)$ and its major and minor radius?
The equation of an ellipse with center $(h, k)$ is $ \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$ We can rewrite the given equation as $\dfrac{(x - 6)^2}{36} + \dfrac{(y - 6)^2}{9} = 1 $ Thus, the center $(h, k) = (6, 6)$ $36$ is bigger than $9$ so the major radius is $\sqrt{36} = 6$ and the minor radius is $\sqrt{9} = 3$.